Linear Regression Diagnostics
I am trying to determine if there is a relationship between a dependent variable y and independent variable x by fitting a least squares regression model.
Scatterplot of data:
Diagnostic plots:
The residuals seem to have constant variance, and there isn't any clear pattern in the residual vs fitted plot. However, the R-squared and the significance of the model fit's coefficients are very low. In this case, are there any nonlinearity issues that needs to be remediated with a transformation or can I conclude that my model is adequate with the correct functional form ?
Here is the summary of the model:
lm(formula = y ~ x, data = data)
Residuals:
Min 1Q Median 3Q Max
-331911 -235678 -145867 30576 1749376
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 2.440e+05 7.037e+04 3.468 0.00135 **
x 1.796e-04 6.206e-04 0.289 0.77385
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 390100 on 37 degrees of freedom
Multiple R-squared: 0.002259, Adjusted R-squared: -0.02471
F-statistic: 0.08378 on 1 and 37 DF, p-value: 0.7739
statistics regression data-analysis linear-regression regression-analysis
edited Nov 23 '18 at 9:10
Jean-Claude Arbaut
14.7k63464
asked Nov 23 '18 at 8:44
joejoe
61
add a comment |
I am trying to determine if there is a relationship between a dependent variable y and independent variable x by fitting a least squares regression model.
Scatterplot of data:
Diagnostic plots:
The residuals seem to have constant variance, and there isn't any clear pattern in the residual vs fitted plot. However, the R-squared and the significance of the model fit's coefficients are very low. In this case, are there any nonlinearity issues that needs to be remediated with a transformation or can I conclude that my model is adequate with the correct functional form ?
Here is the summary of the model:
lm(formula = y ~ x, data = data)
Residuals:
Min 1Q Median 3Q Max
-331911 -235678 -145867 30576 1749376
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 2.440e+05 7.037e+04 3.468 0.00135 **
x 1.796e-04 6.206e-04 0.289 0.77385
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 390100 on 37 degrees of freedom
Multiple R-squared: 0.002259, Adjusted R-squared: -0.02471
F-statistic: 0.08378 on 1 and 37 DF, p-value: 0.7739
statistics regression data-analysis linear-regression regression-analysis
edited Nov 23 '18 at 9:10
Jean-Claude Arbaut
14.7k63464
asked Nov 23 '18 at 8:44
joejoe
61
The scatter plot shows the relation is not clearly linear, and accordingly the p-value for $x$ would lead to remove the variable from the model. I'd say the variability is not well explained by $x$ and you should look for other regressors. Also, the $R^2$ is far too low, which means the model explains only a small fration of the variance of $y$.
– Jean-Claude Arbaut
Nov 23 '18 at 9:02
I completely agree with Jean-Claude Arbaut.
– Adrian Keister
Nov 28 '18 at 13:54
@Jean-ClaudeArbaut: Thanks for the heads-up. I'll take a look. Update: Needed to send to the https version. That fixed the problem. Thanks!
– Adrian Keister
Dec 4 '18 at 23:33
add a comment |
I am trying to determine if there is a relationship between a dependent variable y and independent variable x by fitting a least squares regression model.
Scatterplot of data:
Diagnostic plots:
The residuals seem to have constant variance, and there isn't any clear pattern in the residual vs fitted plot. However, the R-squared and the significance of the model fit's coefficients are very low. In this case, are there any nonlinearity issues that needs to be remediated with a transformation or can I conclude that my model is adequate with the correct functional form ?
Here is the summary of the model:
lm(formula = y ~ x, data = data)
Residuals:
Min 1Q Median 3Q Max
-331911 -235678 -145867 30576 1749376
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 2.440e+05 7.037e+04 3.468 0.00135 **
x 1.796e-04 6.206e-04 0.289 0.77385
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 390100 on 37 degrees of freedom
Multiple R-squared: 0.002259, Adjusted R-squared: -0.02471
F-statistic: 0.08378 on 1 and 37 DF, p-value: 0.7739
statistics regression data-analysis linear-regression regression-analysis
edited Nov 23 '18 at 9:10
Jean-Claude Arbaut
14.7k63464
asked Nov 23 '18 at 8:44
joejoe
61
I am trying to determine if there is a relationship between a dependent variable y and independent variable x by fitting a least squares regression model.
Scatterplot of data:
Diagnostic plots:
The residuals seem to have constant variance, and there isn't any clear pattern in the residual vs fitted plot. However, the R-squared and the significance of the model fit's coefficients are very low. In this case, are there any nonlinearity issues that needs to be remediated with a transformation or can I conclude that my model is adequate with the correct functional form ?
Here is the summary of the model:
lm(formula = y ~ x, data = data)
Residuals:
Min 1Q Median 3Q Max
-331911 -235678 -145867 30576 1749376
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 2.440e+05 7.037e+04 3.468 0.00135 **
x 1.796e-04 6.206e-04 0.289 0.77385
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 390100 on 37 degrees of freedom
Multiple R-squared: 0.002259, Adjusted R-squared: -0.02471
F-statistic: 0.08378 on 1 and 37 DF, p-value: 0.7739
statistics regression data-analysis linear-regression regression-analysis
statistics regression data-analysis linear-regression regression-analysis
edited Nov 23 '18 at 9:10
Jean-Claude Arbaut
14.7k63464
asked Nov 23 '18 at 8:44
joejoe
61
edited Nov 23 '18 at 9:10
Jean-Claude Arbaut
14.7k63464
asked Nov 23 '18 at 8:44
joejoe
61
edited Nov 23 '18 at 9:10
Jean-Claude Arbaut
14.7k63464
edited Nov 23 '18 at 9:10
Jean-Claude Arbaut
14.7k63464
edited Nov 23 '18 at 9:10
Jean-Claude Arbaut
14.7k63464
14.7k63464
asked Nov 23 '18 at 8:44
joejoe
61
asked Nov 23 '18 at 8:44
joejoe
61
asked Nov 23 '18 at 8:44
joejoe
61
61
The scatter plot shows the relation is not clearly linear, and accordingly the p-value for $x$ would lead to remove the variable from the model. I'd say the variability is not well explained by $x$ and you should look for other regressors. Also, the $R^2$ is far too low, which means the model explains only a small fration of the variance of $y$.
– Jean-Claude Arbaut
Nov 23 '18 at 9:02
I completely agree with Jean-Claude Arbaut.
– Adrian Keister
Nov 28 '18 at 13:54
@Jean-ClaudeArbaut: Thanks for the heads-up. I'll take a look. Update: Needed to send to the https version. That fixed the problem. Thanks!
– Adrian Keister
Dec 4 '18 at 23:33
add a comment |
The scatter plot shows the relation is not clearly linear, and accordingly the p-value for $x$ would lead to remove the variable from the model. I'd say the variability is not well explained by $x$ and you should look for other regressors. Also, the $R^2$ is far too low, which means the model explains only a small fration of the variance of $y$.
– Jean-Claude Arbaut
Nov 23 '18 at 9:02
I completely agree with Jean-Claude Arbaut.
– Adrian Keister
Nov 28 '18 at 13:54
@Jean-ClaudeArbaut: Thanks for the heads-up. I'll take a look. Update: Needed to send to the https version. That fixed the problem. Thanks!
– Adrian Keister
Dec 4 '18 at 23:33
The scatter plot shows the relation is not clearly linear, and accordingly the p-value for $x$ would lead to remove the variable from the model. I'd say the variability is not well explained by $x$ and you should look for other regressors. Also, the $R^2$ is far too low, which means the model explains only a small fration of the variance of $y$.
– Jean-Claude Arbaut
Nov 23 '18 at 9:02
The scatter plot shows the relation is not clearly linear, and accordingly the p-value for $x$ would lead to remove the variable from the model. I'd say the variability is not well explained by $x$ and you should look for other regressors. Also, the $R^2$ is far too low, which means the model explains only a small fration of the variance of $y$.
– Jean-Claude Arbaut
Nov 23 '18 at 9:02
I completely agree with Jean-Claude Arbaut.
– Adrian Keister
Nov 28 '18 at 13:54
I completely agree with Jean-Claude Arbaut.
– Adrian Keister
Nov 28 '18 at 13:54
@Jean-ClaudeArbaut: Thanks for the heads-up. I'll take a look. Update: Needed to send to the https version. That fixed the problem. Thanks!
– Adrian Keister
Dec 4 '18 at 23:33
@Jean-ClaudeArbaut: Thanks for the heads-up. I'll take a look. Update: Needed to send to the https version. That fixed the problem. Thanks!
– Adrian Keister
Dec 4 '18 at 23:33
add a comment |
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The scatter plot shows the relation is not clearly linear, and accordingly the p-value for $x$ would lead to remove the variable from the model. I'd say the variability is not well explained by $x$ and you should look for other regressors. Also, the $R^2$ is far too low, which means the model explains only a small fration of the variance of $y$.
– Jean-Claude Arbaut
Nov 23 '18 at 9:02
I completely agree with Jean-Claude Arbaut.
– Adrian Keister
Nov 28 '18 at 13:54
@Jean-ClaudeArbaut: Thanks for the heads-up. I'll take a look. Update: Needed to send to the https version. That fixed the problem. Thanks!
– Adrian Keister
Dec 4 '18 at 23:33